Equatorial Kelvin waves and internal gravity waves were research subjects for both Jim Holton and the present author nearly at the same time. In this talk, after revisiting the research topics in those days then some results of recent numerical experiments conducted by the author's group in which waves have appeared will be presented.

In the late 1960s Holton studied the 3-D structure of the upward propagating Kelvin wave to identify the eastward moving wave in the stratosphere discovered by Wallace and Kousky, soon after the publication of the authors paper on the equatorial waves based on a shallow water model. Then he presented the theory of QBO collaborating with Lindzen by incorporating the westerly acceleration by Kelvin waves. But the source of the wave were left yet to be investigated. In the past decade numerical studies on QBO appeared where the “naturally generated” Kelvin waves by convections in the troposphere are working to cause westerly phase of QBO. On the other hand, the tropospheric Kelvin waves coupled with convection have been studied in connection with MJO. Recent results on convection-coupled Kelvin waves found in global cloud-resolving AGCM experiments will be presented.

In 1982, both Holton and the author presented simple models of the middle atmosphere circulation (the mean zonal winds and the meridional circulation) primarily driven by O3-heating and modified by momentum deposition of upward propagating internal gravity waves immediately after Lindzen's proposal on the effect. The gravity wave drag thus introduced in the middle atmosphere dynamics was quickly applied to the tropospheric AGCMs and NWP models to solve a difficulty at that time. Stationary waves generated by small-scale orography are considered to play a major role. However, in the author's study propagating waves in all directions were considered. Recently direct numerical modeling with high-resolution AGCM was made in the author's group. Some results of the experiment will be reported.